A parabolic Littlewood-Paley inequality with applications to parabolic equations

A critical parabolic Sobolev embedding via Littlewood-Paley decomposition

In this paper, we show a parabolic version of the Ogawa type inequality in Sobolev spaces. Our inequality provides an estimate of the L∞ norm of a function in terms of its parabolic BMO norm, with the aid of the square root of the logarithmic dependency of a higher order Sobolev norm. The proof is mainly based on the Littlewood-Paley decomposition and a characterization of parabolic BMO spaces....

Multilinear Littlewood-Paley estimates with applications to partial differential equations.

We obtain a collection of multilinear Littlewood-Paley estimates, which we then apply to two problems in partial differential equations. The first problem is the estimation of the square root of an elliptic operator in divergence form, and the second is the estimation of solutions to the Cauchy problem for nondivergence-form parabolic equations.

Littlewood–Paley Inequality: A Survey

Let Sωf = ∫ ω f̂(ξ)e ixξ dξ be the Fourier projection operator to an interval ω in the real line. Rubio de Francia’s Littlewood Paley inequality [31] states that for any collection of disjoint intervals Ω, we have ∥∥ [∑ ω∈Ω |Sωf | 1/2∥∥ p . ‖f‖p, 2 ≤ p < ∞. We survey developments related to this inequality, including the higher dimensional case, and consequences for multipliers.

A Semi-discrete Littlewood-paley Inequality

Issues related to Rubio de Francia’s Littlewood–Paley inequality

Let Sω f = ∫ ω f̂(ξ)e dξ be the Fourier projection operator to an interval ω in the real line. Rubio de Francia’s Littlewood–Paley inequality (Rubio de Francia, 1985) states that for any collection of disjoint intervals Ω, we have ∥∥∥∥ [∑ ω∈Ω |Sω f | 1/2∥∥∥∥ p ‖f‖p, 2 ≤ p < ∞. We survey developments related to this inequality, including the higher dimensional case, and consequences for multiplie...